MATH 0413
HW02
Due Thursday, September 17
Problems 17 will be collected and graded.
Problem 1. Let A = N and B denote the set of all odd integers 11. Show that |A| = |B|.
Problem 2. Prove that f (x) =
Problem 3. Prove
for all n N.
2x
is a bijection from [

HW01 Hints
In order to eectively improve ones ability in constructing proofs, one
should attempt each problem (for 30 minutes) before reading hints.
After reading one step of the hint, it would be a good idea to attempt the
problem again before reading ad

Math 0413 (TuTh 6:00-7:15pm) Term Paper
The term paper is due in class at 7:15pm on Tuesday, December 8, 2015.
The length should be 4 to 6 pages. All sources must be cited in the paper. Papers that include passages lifted verbatim from other sources witho

Evan Bair
Homework 2
Dr. Sati
29 Jan. 2015
0.3.2
Induction:
(i) P(1) is true,
(ii) if P(n) is true, then P(n+1) is true (denoted by A)
Then P(n) is true for all n N
Strong Induction:
(i) P(n) is true,
(ii) if P(k) is true for all k=1,2,.,n, then P(n+1) is

MATH 0413
HW 4
Due Monday, May 23
Problem 1. Prove that, if a, b R, then ab = (a)(b). You may use the items from the list of
axioms and theorems on Page 2 only. Identify the item(s) used in each step. Include only the ones
that are actually needed.
Proble

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This class is very valuable if you wish to pursue mathematics or simply gain a better understanding of the construction of mathematical theorems. It teaches you how to write proofs vigorously and gives you fundamental knowledge of the properties that have been used in other math classes. Lastly, it is different from most math classes you have taken. It is less about computations and more about thinking through abstract problems while only using the theorems given to you.

Course highlights:

This course taught me how to think through theoretical problems, apply material from lectures in more abstract ways, and write detailed proofs using proper notation. The highlights of the course include an introduction to set theory, a fundamental understanding of countable, countably infinite, and uncountable sets, and an in depth explanation of limits, sequences, and series. Finally, the course gives you a solid base to build upon in future theoretical math classes.

Hours per week:

9-11 hours

Advice for students:

Pay attention to the lectures and understand how the professor utilizes the theorems in the textbook to complete the examples. If you have time, go through the examples again on your own and rewrite them to get a good feel for the proof writing process. Recitations are not required, but are very valuable because they are filled with examples that utilize the theorems and help you with the homework. Homework is incredibly important and should be given plenty of attention in order to properly grasp the proof writing process as well as the theorems you will need to use for the tests. Also, you should write several drafts of your homework to make sure the theorems, definitions, and notations are used properly. Lastly, the math assistance center is your best friend for this class, but make sure you are seeing students that can teach you the material instead of simply giving you the answers.

Course Term:Spring 2016

Professor:Dehua Wang

Course Tags:Math-heavyLots of WritingAlways Do the Reading

Feb 17, 2016

| Would recommend.

This class was tough.

Course Overview:

This class is definitely a challenge. It is used many ways throughout your career. It'll help you understand the fundamentals of mathematical analysis and prepare you for more challenging courses in the future. I recommend this course to those who want to advance in mathematics.

Course highlights:

This course began with set theory. It moved to different topics like bounds, basic proofs with induction, contradiction, etc. The end of the term was specifically geared toward series and sequences.

Hours per week:

9-11 hours

Advice for students:

Don't miss a class and work on proofs. Learn the fundamentals, such as theorems, axioms, lemmas, collaries, etc. It's all important and will help you work through the problems more efficiently and correctly.